It was the atmosphere in the home dressing room at half-time that damned West Ham United most of all. Scott Parker had struck a Wolverhampton Wanderers upright in the seconds before the interval on Tuesday night. Though they were still a goal down, that clear-cut opportunity could have carried them through the team-talk and fuelled conviction that the deficit could be clawed back and relegation rivals overcome. It was a moment for players and coaching staff to offer back-slapping encouragement and raucous gee-ups. Instead there was numbed silence.

The reaction said everything. "The manager tried but everyone's head had dropped," admitted Benni McCarthy. "We hadn't performed and everyone was hiding their head in their shirts, too shy to show their faces. It was really hard. It's hard to know what to say any more because it was just shocking. At least we've reached rock bottom. We can't get any lower than this. But we didn't expect that performance."

The second-half display was easier to explain in that shoddy context. The capitulation, when it came around the hour-mark, shredded what little confidence remained. West Ham are one place – and three points – above the relegation zone and a sense of panic is spreading. That was expressed by the owners, David Sullivan and David Gold, in their post-match meeting with Gianfranco Zola, the Italian crestfallen and dumbfounded by the mishmash he had just witnessed. The prospect of demotion to the Championship, with its cataclysmic financial implications, is unthinkable at the Boleyn Ground. This team has to survive but, on this evidence, they may do so only courtesy of the deficiencies of those below them.

The knee-jerk reaction would be to dismiss the club's manager of 18 months, particularly as he was appointed by the ancien régime at Upton Park. But Zola and his assistant, Steve Clarke, signed new three-year deals only last May and, with annual salaries of around £1.9m and £900,000 respectively, compensation would be hefty. Perhaps more significant is that no obvious short-term replacements stand out. The Premier League's "impact manager of the moment" is Iain Dowie, a man still living off a reputation forged largely over five giddy months in the second tier at Crystal Palace in 2004. There appears to be a lack of firefighters available.

The hope remains that a relatively paltry points tally should be enough to survive this season, given the inadequacies of Portsmouth, Burnley and Hull City. Yet, with Dowie's Hull still to host Fulham, Burnley and Sunderland – hardly easy fixtures but potentially winnable – West Ham desperately need to eke out breathing space and, judging by events against Wolves, they are imploding. Zola heaped the blame upon himself in the wake of his side's fifth consecutive reverse, stressing his players had tried, albeit in "a disorganised way". Defensively they had been shambolic. Clarke was much loved, and hugely rated, at Chelsea for his ability to instil defensive sureness into a side. His reputation is being tarnished by this term's toils.

Too much pressure is being heaped on James Tomkins, a highly promising young player who is prone to mistakes such as that which presented Kevin Doyle with Wolves' opening goal on Tuesday. More experienced colleagues such as Danny Gabbidon and Manuel da Costa have been affected by injuries and suspensions. Yet, the defence receives precious little support from those up-field. West Ham's wingers in the second half against Wolves, Junior Stanislas and Alessandro Diamanti, failed utterly to track back, so anxious were they to make inroads at the other end. The defence was left horribly exposed.

The rather frenzied approach, all desperate head-down charges into enemy territory with little pattern or precision to their game, merely added to the general sense of chaos. At one stage in the first half on Tuesday, Wolves – newly promoted and expected to struggle, but now settled and organised – pinged passes amongst themselves at will while the hosts gasped in pursuit of the ball. The move culminated with the excellent David Jones forcing Rob Green to save. But, where Wolves' patience went rewarded, West Ham's desperation always felt destined to yield negligible reward.

Zola recognises the problems. "They've been trying and have worked very hard but more as individuals than as a team," he conceded. "Making them play as a team is my responsibility." But so fragile is confidence in this corner of east London, with the supporters gripped by anxiety and ready to turn, that performances are wrecked and games surrendered on errors such as Tomkins' scuffed back-pass. Tuesday's game ended with a chorus of boos, Carlton Cole remonstrating with one fan and chants of "You're not fit to wear the shirt". All faith in this team's ability appears to have been lost.

"An error from us and then everyone lost their heads," said McCarthy. "Then the fans started showing their frustration and it made things even worse on the pitch. No one in the dressing room wants to be hearing what went down in the stands.Even if you know there's so much at stake, it's difficult to take. But we should have done better.We're professionals and we should have shown our character and changed people's minds. Instead We let it affect us. Everyone started hiding a little bitand that's no way to go about it when things aren't going your way."

Stoke City visit Upton Park on Saturday. A repeat of Tuesday's fiasco will not be tolerated by either owners or supporters. The club teeters on the brink.